Scaling and self-similarity in one-dimensional unsteady open channel flow

2014-02-01
Ercan, Ali
Kavvas, M. Levent
Haltas, Ismail
Show full item record
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
81
views
0
downloads
The conditions under which the Saint Venant equations system for unsteady open channel flow, as an initial-boundary value problem, becomes self-similar are investigated by utilizing one-parameter Lie group of point scaling transformations. One of the advantages of this methodology is that the self-similarity conditions due to the initial and boundary conditions can also be investigated thoroughly in addition to the conditions due to the governing equation. The obtained self-similarity conditions are compared with the scaling relationships that are derived through the Froude similitude. It is shown that the initial-boundary value problem of a one-dimensional unsteady open channel flow process in a prototype domain can be self-similar with that of several different scaled domains. However, the values of all the flow variables (at specified time and space) under different scaled domains can be upscaled to the same values in the prototype domain (at the corresponding time and space), as shown in this study. Distortion in scales of different space dimensions has been implemented extensively in physical hydraulic modelling, mainly because of cost, space and time limitations. Unlike the traditional approach, the distinction is made between the longitudinal-horizontal and transverse-horizontal length scales in this study. The scaled domain obtained by the proposed approach, when scaling ratios of channel width and water depth are equal, is particularly important for the similarity of flow characteristics in a cross-section because the width-to-depth ratio and the inclination angles of the banks are conserved in a cross-section. It is also shown that the scaling ratio of the roughness coefficient under distorted channel conditions depends on that of hydraulic radius and longitudinal length. The proposed scaling relations obtained by the Lie group scaling approach may provide additional spatial, temporal and economical flexibility in setting up physical hydraulic models. Copyright (c) 2013 John Wiley & Sons, Ltd.
scaling, self-similarity, Saint Venant equations, scale-invariance, similitude, INVARIANCE, SPACE, TIME
https://hdl.handle.net/11511/99838
HYDROLOGICAL PROCESSES
Department of Civil Engineering, Article

Suggestions

Scaling and self-similarity in two-dimensional hydrodynamics
Ercan, Ali; Kavvas, M. Levent (2015-07-01)
The conditions under which depth-averaged two-dimensional (2D) hydrodynamic equations system as an initial-boundary value problem (IBVP) becomes self-similar are investigated by utilizing one-parameter Lie group of point scaling transformations. Self-similarity conditions due to the 2D k-epsilon turbulence model are also investigated. The self-similarity conditions for the depth-averaged 2D hydrodynamics are found for the flow variables including the time, the longitudinal length, the transverse length, the...
Model order reduction for pattern formation in reaction-diffusion systems
Karasözen, Bülent; Küçükseyhan, Tuğba; Mülayim, Gülden (null; 2017-09-22)
We compare three reduced order modelling (ROM) techniques: the proper orthogonal decomposition (POD), discrete empirical interpolation (DEIM) [2], and dynamical mode decomposition (DMD) [1] to reaction diusion equations in biology. The formation of patterns in reaction-diusion equations require highly accurate solutions in space and time and therefore require large computational time to reach the steady states. The three reduced order methods are applied to the diusive FitzHugh-Nagumo equation [3] and th...
Scaling Relations and Self-Similarity of 3-Dimensional Reynolds-Averaged Navier-Stokes Equations
Ercan, Ali; Kavvas, M. Levent (2017-07-01)
Scaling conditions to achieve self-similar solutions of 3-Dimensional (3D) Reynolds-Averaged Navier-Stokes Equations, as an initial and boundary value problem, are obtained by utilizing Lie Group of Point Scaling Transformations. By means of an open-source Navier-Stokes solver and the derived self-similarity conditions, we demonstrated self-similarity within the time variation of flow dynamics for a rigid-lid cavity problem under both up-scaled and down-scaled domains. The strength of the proposed approach ...
Signaling Games for Log-Concave Distributions: Number of Bins and Properties of Equilibria
Kazikli, Ertan; Sarıtaş, Serkan; GEZİCİ, Sinan; Linder, Tamas; Yuksel, Serdar (2022-03-01)
We investigate the equilibrium behavior for the decentralized cheap talk problem for real random variables and quadratic cost criteria in which an encoder and a decoder have misaligned objective functions. In prior work, it has been shown that the number of bins in any equilibrium has to be countable, generalizing a classical result due to Crawford and Sobel who considered sources with density supported on [0, 1]. In this paper, we first refine this result in the context of log-concave sources. For sources ...
Chaos in planar oscillations of a Toda particle
Yavas, O; Akkas, N (1996-04-01)
The dynamic behaviour of a Toda particle is investigated numerically. The system is a discrete spring-mass system and it oscillates in a plane two-dimensionally under the action of a harmonic excitation. Periodic and chaotic motions are shown to be possible in the parameter space. Numerical methods are used to obtain the time histories, the Poincare maps, the Lyapunov spectra, their fractal dimensions and the power spectra. It is shown that the system is sensitive to initial conditions. The two- and three-d...
Citation Formats
A. Ercan, M. L. Kavvas, and I. Haltas, “Scaling and self-similarity in one-dimensional unsteady open channel flow,” HYDROLOGICAL PROCESSES, vol. 28, no. 5, pp. 2721–2737, 2014, Accessed: 00, 2022. [Online]. Available: https://hdl.handle.net/11511/99838.
METU IIS - Integrated Information Service open@metu.edu.tr